I have only played one game so far and we put our used order tokens face upp in front of the player screen. The downside to this is that you can deduct what tokens the other players have left and act accordingly (at least in the later rounds).

You played it by the rules. If you look at the first paragraph of p.9 it says that the discard pile is a faceup pile near the player who played the token.

It seems intentional that players can and should be paying attention to what resources their opponents have left. It makes the end game feel a little like chess while avoiding a potentially formulaic early game by introducing a diminishing amount of randomness.